While hierarchical linear modeling is often used in social science research, the assumption of normally distributed residuals at the individual and cluster levels can be violated in empirical data. Previous studies have focused on the effects of nonnormality at either lower or higher level(s) separately. However, the violation of the normality…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

A multilevel Rasch model using a hierarchical generalized linear model is one approach to multilevel item response theory (IRT) modeling and is referred to as a one-parameter hierarchical generalized linear logistic model (1-P HGLLM). Although it has the flexibility to model nested structure of data with covariates, the model assumes the normality…

Interest in variation in program impacts--How big is it? What might explain it?--has inspired recent work on the analysis of data from multi-site experiments. One critical aspect of this problem involves the use of random or fixed effect estimates to visualize the distribution of impact estimates across a sample of sites. Unfortunately, unless the…